Question

a bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. the tire pressure is currently 1,060 kilopascals. what will it be in 4 minutes? if necessary, round your answer to the nearest tenth. kilopascals

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $P(t) = P_0(1 - r)^t$, where $P_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time elapsed.
Here, $P_0 = 1060$ kilopascals, $r = 0.10$ (since 10% = 0.10), and $t = 4$ minutes.

Step2: Substitute the values into the formula

Substitute $P_0 = 1060$, $r = 0.10$, and $t = 4$ into the formula:
$P(4) = 1060(1 - 0.10)^4$

Step3: Simplify the expression inside the parentheses

First, calculate $1 - 0.10 = 0.90$. So the formula becomes:
$P(4) = 1060(0.90)^4$

Step4: Calculate $(0.90)^4$

$(0.90)^4 = 0.90\times0.90\times0.90\times0.90 = 0.6561$

Step5: Multiply by the initial pressure

Now, multiply 1060 by 0.6561:
$P(4) = 1060\times0.6561 = 695.466$

Step6: Round to the nearest tenth

Rounding 695.466 to the nearest tenth gives 695.5.

Answer:

695.5